College Algebra, 2013a

156 Linear and Quadratic Functions
Definition 2.1. A linear function is a function of the form
f(x) =mx + b,
where m and b are real numbers with m ≠ 0. The domain of a linear function is (−∞, ∞).
For the case m =0,wegetf(x) =b. These are given their own classification.
Definition 2.2. A constant function is a function of the form
f(x) =b,
where b is real number. The domain of a constant function is (−∞, ∞).
Recall that to graph a function, f, we graph the equation y = f(x). Hence, the graph of a
linear function is a line with slope m and y-intercept (0,b); the graph of a constant function is a
horizontal line (a line with slope m =0)anday-intercept of (0,b). Now think back to Section 1.6.1,
specifically Definition 1.10 concerning increasing, decreasing and constant functions. A line with
positive slope was called an increasing line because a linear function with m>0 is an increasing
function. Similarly, a line with a negative slope was called a decreasing line because a linear function
with m